Chapter 7: Q. 2 (page 655)
Fill in the blanks.
For r_____ , the sequence converges to _____.
Short Answer
The required answer is for , the sequence converges to 1 and for , the sequence converges to 0.
Chapter 7: Q. 2 (page 655)
Fill in the blanks.
For r_____ , the sequence converges to _____.
The required answer is for , the sequence converges to 1 and for , the sequence converges to 0.
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Get started for freeDetermine whether the series converges or diverges. Give the sum of the convergent series.
For each series in Exercises 44–47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder,.
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that
Given thatand, find the value of.
Given a series , in general the divergence test is inconclusive when . For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.
Letand be two convergent geometric series. If b and v are both nonzero, prove that is a geometric series. What condition(s) must be met for this series to converge?
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